Productivity rankings for English derivational suffixes

@cite{odonnell-2015}

Theory-neutral observations about three English nominalising suffixes — -ness, -ion, -ate — that @cite{odonnell-2015} Chapter 7 uses as the central empirical contrast for evaluating the five FG-family models. The three suffixes are chosen because intuitive judgments and earlier literature converge: -ness:Adj>N is highly productive (e.g. pine-scentedness); -ion:V>N is unproductive despite high token frequency (*meetion — see @cite{odonnell-2015} p. 261); -ate:BND>V is restricted to bound stems and so cannot productively attach to novel verbs.

The book's central Chapter 7 empirical claim (Fig 7.3, p. 262; Table 7.1, p. 265) is that only the FG model places -ness in its top-5 most productive suffixes, and all four competing models (DMPCFG, MAG, DOP1, ENDOP) wrongly predict -ion as highly productive, with three of them (DMPCFG, DOP1, ENDOP) also wrongly predicting -ate as productive. The intuitive ordering of productivity is ness > ion ≈ ate (the latter two both unproductive, distinguished only by selectional restrictions).

The book's frequency-spectrum facts (Fig 7.4, p. 267; Fig 1.1, p. 20 in the introduction) supply the distributional evidence: -ness has the LNRE shape characteristic of a productive process (many low-frequency types, hapax-rich); -ion and -ate do not.

This file states the qualitative rankings and spectrum shapes; specific token-frequency values (e.g. the maxima visible in Fig 7.4) are not formalized — per CLAUDE.md, regression-summary numbers belong in prose.

What's here

• Suffix — the three suffixes
• PeakLocation, TypeTokenRatio — qualitative bins for the spectrum
• SuffixSpectrum — the three properties of the empirical spectrum
• observed — the spectrum shape attributed to each suffix
• Suffix.productivityIndex — pre-theoretic numeric ranking
• moreProductiveThan — strict ordering on suffixes; theories must reproduce this to match @cite{odonnell-2015} Fig 7.3

These data are picked up downstream by Studies files that bridge them to predictions of the various probabilistic-grammar models.

Theory neutrality

This file contains no theoretical interpretation. The terms "productive" and "unproductive" used in the docstring above are pre-theoretic descriptions consistent with the literature @cite{odonnell-2015} reviews; the file commits to nothing about why one suffix is productive and another is not. Theories that account for the observed pattern import this data and produce explanations.

The "large number of rare events" classification in SuffixSpectrum.isLNRE is a distributional property attributed in @cite{odonnell-2015} to a broader literature on word-frequency distributions; it is not itself a theoretical commitment about the mechanism that gives rise to such distributions.

inductive Phenomena.Morphology.Productivity.Suffix : Type

The three English derivational suffixes that @cite{odonnell-2015} Chapter 7 uses as the central productivity contrast.

• -ness (Adj>N): highly productive (tall → tallness, pine-scented → pine-scentedness).
• -ion (V>N): high token frequency but unproductive on novel verbs (*meetion — Ch 7 p. 261).
• -ate (BND>V): restricted to bound stems (e.g. segregate from segregat-); cannot productively attach to free verbs.

• ness : Suffix
• ion : Suffix
• ate : Suffix

@[implicit_reducible]

instance Phenomena.Morphology.Productivity.instDecidableEqSuffix : DecidableEq Suffix

Equations

• Phenomena.Morphology.Productivity.instDecidableEqSuffix x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[implicit_reducible]

instance Phenomena.Morphology.Productivity.instReprSuffix : Repr Suffix

Equations

• Phenomena.Morphology.Productivity.instReprSuffix = { reprPrec := Phenomena.Morphology.Productivity.instReprSuffix.repr }

def Phenomena.Morphology.Productivity.instReprSuffix.repr : Suffix → Nat → Std.Format

Equations

• One or more equations did not get rendered due to their size.

inductive Phenomena.Morphology.Productivity.PeakLocation : Type

Where the mass of a word-frequency spectrum is concentrated. A spectrum peaked at low frequencies indicates a large number of low-token-count types — characteristic of a productive process that generates many novel coinages. A spectrum spread toward higher frequencies indicates that the relevant types are mostly common existing words rather than novel coinages.

• low : PeakLocation
• mid : PeakLocation
• high : PeakLocation

@[implicit_reducible]

instance Phenomena.Morphology.Productivity.instDecidableEqPeakLocation : DecidableEq PeakLocation

Equations

• Phenomena.Morphology.Productivity.instDecidableEqPeakLocation x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

@[implicit_reducible]

instance Phenomena.Morphology.Productivity.instReprPeakLocation : Repr PeakLocation

Equations

• Phenomena.Morphology.Productivity.instReprPeakLocation = { reprPrec := Phenomena.Morphology.Productivity.instReprPeakLocation.repr }

def Phenomena.Morphology.Productivity.instReprPeakLocation.repr : PeakLocation → Nat → Std.Format

Equations

• One or more equations did not get rendered due to their size.

inductive Phenomena.Morphology.Productivity.TypeTokenRatio : Type

Type-token ratio class. high = many distinct types each with low token count; low = few types each with high token count. The ratio is itself a coarse proxy for productivity: productive processes generate many novel types, raising the ratio.

• high : TypeTokenRatio
• mid : TypeTokenRatio
• low : TypeTokenRatio

@[implicit_reducible]

instance Phenomena.Morphology.Productivity.instDecidableEqTypeTokenRatio : DecidableEq TypeTokenRatio

Equations

• Phenomena.Morphology.Productivity.instDecidableEqTypeTokenRatio x✝ y✝ = if h : x✝.ctorIdx = y✝.ctorIdx then isTrue ⋯ else isFalse ⋯

def Phenomena.Morphology.Productivity.instReprTypeTokenRatio.repr : TypeTokenRatio → Nat → Std.Format

Equations

• One or more equations did not get rendered due to their size.

@[implicit_reducible]

instance Phenomena.Morphology.Productivity.instReprTypeTokenRatio : Repr TypeTokenRatio

Equations

• Phenomena.Morphology.Productivity.instReprTypeTokenRatio = { reprPrec := Phenomena.Morphology.Productivity.instReprTypeTokenRatio.repr }

structure Phenomena.Morphology.Productivity.SuffixSpectrum : Type

Qualitative properties of the word-frequency spectrum for words formed by some derivational process.

The isLNRE flag marks the "large number of rare events" classification of word-frequency distributions used in @cite{odonnell-2015} as a diagnostic for productive processes: a distribution where most types are singletons or near-singletons and the tail extends far is the distributional fingerprint of an active word-formation process.

• peak : PeakLocation
• isLNRE : Bool
• typeTokenRatio : TypeTokenRatio

theorem Phenomena.Morphology.Productivity.SuffixSpectrum.ext {x y : SuffixSpectrum} (peak : x.peak = y.peak) (isLNRE : x.isLNRE = y.isLNRE) (typeTokenRatio : x.typeTokenRatio = y.typeTokenRatio) : x = y

theorem Phenomena.Morphology.Productivity.SuffixSpectrum.ext_iff {x y : SuffixSpectrum} : x = y ↔ x.peak = y.peak ∧ x.isLNRE = y.isLNRE ∧ x.typeTokenRatio = y.typeTokenRatio

@[implicit_reducible]

instance Phenomena.Morphology.Productivity.instDecidableEqSuffixSpectrum : DecidableEq SuffixSpectrum

Equations

• Phenomena.Morphology.Productivity.instDecidableEqSuffixSpectrum = Phenomena.Morphology.Productivity.instDecidableEqSuffixSpectrum.decEq

def Phenomena.Morphology.Productivity.instDecidableEqSuffixSpectrum.decEq (x✝ x✝¹ : SuffixSpectrum) : Decidable (x✝ = x✝¹)

Equations

• One or more equations did not get rendered due to their size.

def Phenomena.Morphology.Productivity.instReprSuffixSpectrum.repr : SuffixSpectrum → Nat → Std.Format

Equations

• One or more equations did not get rendered due to their size.

@[implicit_reducible]

instance Phenomena.Morphology.Productivity.instReprSuffixSpectrum : Repr SuffixSpectrum

Equations

• Phenomena.Morphology.Productivity.instReprSuffixSpectrum = { reprPrec := Phenomena.Morphology.Productivity.instReprSuffixSpectrum.repr }

def Phenomena.Morphology.Productivity.observed : Suffix → SuffixSpectrum

The three spectra shown qualitatively in @cite{odonnell-2015} Figure 7.4 (p. 267) and discussed in Chapter 7.

• -ness: low-frequency peak, LNRE shape, high type-token ratio (productive — the only one of the three placed in any model's top-5 by the FG model).
• -ion: peak shifted toward high frequencies, no LNRE shape, low type-token ratio (despite ~1117 word types, the distribution is dominated by high-frequency lemmas; not productive in the novel-coinage sense).
• -ate: similar high-frequency shape as -ion, restricted to bound stems (cannot attach to free verbs at all, so productivity on novel free-verb stems is structurally zero).

Equations

• One or more equations did not get rendered due to their size.

def Phenomena.Morphology.Productivity.Suffix.productivityIndex : Suffix → Nat

A pre-theoretic productivity index for the three suffixes — higher is more productive. Used as the basis for moreProductiveThan.

Coding ness > ion > ate reproduces the ordering implied by @cite{odonnell-2015} Chapter 7 (Fig 7.3, Table 7.1, the §7.3.1.1 discussion). The ion > ate direction is a tie-break: both are unproductive on novel forms, but ate is structurally more restricted (bound stems only), so we rank it strictly lower.

Equations

• Phenomena.Morphology.Productivity.Suffix.ness.productivityIndex = 2
• Phenomena.Morphology.Productivity.Suffix.ion.productivityIndex = 1
• Phenomena.Morphology.Productivity.Suffix.ate.productivityIndex = 0

def Phenomena.Morphology.Productivity.moreProductiveThan (a b : Suffix) : Prop

The pre-theoretic strict ordering on the three suffixes by productivity. Any theory of productivity that purports to account for the @cite{odonnell-2015} Chapter 7 data must reproduce this ordering; failure to do so falsifies the theory against the data (this is exactly the discriminator deployed against DMPCFG / MAG / DOP1 / ENDOP in @cite{odonnell-2015} Fig 7.3, all of which place -ion in their top 5).

Defined as > on Suffix.productivityIndex, which gives decidability and the standard order properties for free.

Equations

• Phenomena.Morphology.Productivity.moreProductiveThan a b = (a.productivityIndex > b.productivityIndex)

@[implicit_reducible]

instance Phenomena.Morphology.Productivity.instDecidableRelSuffixMoreProductiveThan : DecidableRel moreProductiveThan

Equations

• Phenomena.Morphology.Productivity.instDecidableRelSuffixMoreProductiveThan a b = Phenomena.Morphology.Productivity.instDecidableRelSuffixMoreProductiveThan._aux_1 a b